Bridge formula calculator
Enter your axle spacings and weights and every group of axles is checked against the federal bridge formula, the 20,000 lb single and 34,000 lb tandem limits and the 80,000 lb gross. Or look up the most weight a group of axles can carry, or the spacing it needs.
Inputs
Result
Every axle group checked
Each line is a run of consecutive axles. The bridge formula applies to every group of two or more, not just the whole truck. Failing groups are marked.
| Axles | Span | Weight | Limit | Margin | Rule |
|---|
The federal bridge formula
Congress wrote the formula into federal law in 1975 to stop heavy trucks overstressing bridges. A bridge feels a load less when it is spread over more axles and a longer distance, so the formula rewards both. It applies on the Interstate system and is used in some form by most states.
It applies to every group of two or more consecutive axles, not just the whole truck. A 5-axle tractor-trailer has ten groups to check, from the drive tandem alone to all five axles. A truck can pass on gross weight and still fail on one inner group, which is the usual way to get a ticket at a scale.
The other federal limits
- Single axle: 20,000 lb. Axles 40 inches apart or less count as one axle.
- Tandem: 34,000 lb on two axles more than 40 and no more than 96 inches apart.
- Gross: 80,000 lb on the Interstate.
- Two tandems, 36 ft: two consecutive tandems can carry 34,000 lb each when the first and last of those four axles are 36 ft or more apart, even though the formula alone gives 66,000 lb at 36 ft.
Why 51 feet matters
A 5-axle truck can only gross 80,000 lb when the steer axle and the last trailer axle are at least 51 ft apart; at 50 ft the formula allows 79,000. The inner bridge matters too: with the trailer tandems slid forward so the drive and trailer tandems are only 33 ft apart, those four axles are limited to 64,000 lb, not 68,000. That is why drivers slide the tandems back before a heavy load, and why the calculator flags it.
How the numbers are rounded
FHWA rounds W to the nearest 500 lb, and exact halves go down: three axles at 9 ft works out at 42,750 lb and the federal figure is 42,500. Distances are taken to the nearest foot. The table below follows the same rules.
Bridge formula table
The most weight in pounds on a group of axles, by the distance between its outer axles. Two-axle groups up to 8 ft are tandems (34,000 lb). Values stop at 20,000 lb per axle and 80,000 lb gross.
| Distance | 2 axles | 3 axles | 4 axles | 5 axles | 6 axles | 7 axles |
|---|---|---|---|---|---|---|
| 4 ft | 34,000 | 39,000 | 44,500 | 50,500 | 56,500 | 62,500 |
| 5 ft | 34,000 | 39,500 | 45,500 | 51,000 | 57,000 | 63,000 |
| 6 ft | 34,000 | 40,500 | 46,000 | 51,500 | 57,500 | 63,500 |
| 7 ft | 34,000 | 41,000 | 46,500 | 52,500 | 58,000 | 64,000 |
| 8 ft | 34,000 | 42,000 | 47,500 | 53,000 | 59,000 | 64,500 |
| 9 ft | 39,000 | 42,500 | 48,000 | 53,500 | 59,500 | 65,000 |
| 10 ft | 40,000 | 43,500 | 48,500 | 54,000 | 60,000 | 66,000 |
| 11 ft | 40,000 | 44,000 | 49,500 | 55,000 | 60,500 | 66,500 |
| 12 ft | 40,000 | 45,000 | 50,000 | 55,500 | 61,000 | 67,000 |
| 13 ft | 40,000 | 45,500 | 50,500 | 56,000 | 62,000 | 67,500 |
| 14 ft | 40,000 | 46,500 | 51,500 | 56,500 | 62,500 | 68,000 |
| 15 ft | 40,000 | 47,000 | 52,000 | 57,500 | 63,000 | 68,500 |
| 16 ft | 40,000 | 48,000 | 52,500 | 58,000 | 63,500 | 69,500 |
| 17 ft | 40,000 | 48,500 | 53,500 | 58,500 | 64,000 | 70,000 |
| 18 ft | 40,000 | 49,500 | 54,000 | 59,000 | 65,000 | 70,500 |
| 19 ft | 40,000 | 50,000 | 54,500 | 60,000 | 65,500 | 71,000 |
| 20 ft | 40,000 | 51,000 | 55,500 | 60,500 | 66,000 | 71,500 |
| 21 ft | 40,000 | 51,500 | 56,000 | 61,000 | 66,500 | 72,000 |
| 22 ft | 40,000 | 52,500 | 56,500 | 61,500 | 67,000 | 73,000 |
| 23 ft | 40,000 | 53,000 | 57,500 | 62,500 | 68,000 | 73,500 |
| 24 ft | 40,000 | 54,000 | 58,000 | 63,000 | 68,500 | 74,000 |
| 25 ft | 40,000 | 54,500 | 58,500 | 63,500 | 69,000 | 74,500 |
| 26 ft | 40,000 | 55,500 | 59,500 | 64,000 | 69,500 | 75,000 |
| 27 ft | 40,000 | 56,000 | 60,000 | 65,000 | 70,000 | 75,500 |
| 28 ft | 40,000 | 57,000 | 60,500 | 65,500 | 71,000 | 76,500 |
| 29 ft | 40,000 | 57,500 | 61,500 | 66,000 | 71,500 | 77,000 |
| 30 ft | 40,000 | 58,500 | 62,000 | 66,500 | 72,000 | 77,500 |
| 31 ft | 40,000 | 59,000 | 62,500 | 67,500 | 72,500 | 78,000 |
| 32 ft | 40,000 | 60,000 | 63,500 | 68,000 | 73,000 | 78,500 |
| 33 ft | 40,000 | 60,000 | 64,000 | 68,500 | 74,000 | 79,000 |
| 34 ft | 40,000 | 60,000 | 64,500 | 69,000 | 74,500 | 80,000 |
| 35 ft | 40,000 | 60,000 | 65,500 | 70,000 | 75,000 | 80,000 |
| 36 ft | 40,000 | 60,000 | 66,000 | 70,500 | 75,500 | 80,000 |
| 37 ft | 40,000 | 60,000 | 66,500 | 71,000 | 76,000 | 80,000 |
| 38 ft | 40,000 | 60,000 | 67,500 | 71,500 | 77,000 | 80,000 |
| 39 ft | 40,000 | 60,000 | 68,000 | 72,500 | 77,500 | 80,000 |
| 40 ft | 40,000 | 60,000 | 68,500 | 73,000 | 78,000 | 80,000 |
| 41 ft | 40,000 | 60,000 | 69,500 | 73,500 | 78,500 | 80,000 |
| 42 ft | 40,000 | 60,000 | 70,000 | 74,000 | 79,000 | 80,000 |
| 43 ft | 40,000 | 60,000 | 70,500 | 75,000 | 80,000 | 80,000 |
| 44 ft | 40,000 | 60,000 | 71,500 | 75,500 | 80,000 | 80,000 |
| 45 ft | 40,000 | 60,000 | 72,000 | 76,000 | 80,000 | 80,000 |
| 46 ft | 40,000 | 60,000 | 72,500 | 76,500 | 80,000 | 80,000 |
| 47 ft | 40,000 | 60,000 | 73,500 | 77,500 | 80,000 | 80,000 |
| 48 ft | 40,000 | 60,000 | 74,000 | 78,000 | 80,000 | 80,000 |
| 49 ft | 40,000 | 60,000 | 74,500 | 78,500 | 80,000 | 80,000 |
| 50 ft | 40,000 | 60,000 | 75,500 | 79,000 | 80,000 | 80,000 |
| 51 ft | 40,000 | 60,000 | 76,000 | 80,000 | 80,000 | 80,000 |
| 52 ft | 40,000 | 60,000 | 76,500 | 80,000 | 80,000 | 80,000 |
| 53 ft | 40,000 | 60,000 | 77,500 | 80,000 | 80,000 | 80,000 |
| 54 ft | 40,000 | 60,000 | 78,000 | 80,000 | 80,000 | 80,000 |
| 55 ft | 40,000 | 60,000 | 78,500 | 80,000 | 80,000 | 80,000 |
| 56 ft | 40,000 | 60,000 | 79,500 | 80,000 | 80,000 | 80,000 |
| 57 ft | 40,000 | 60,000 | 80,000 | 80,000 | 80,000 | 80,000 |
| 58 ft | 40,000 | 60,000 | 80,000 | 80,000 | 80,000 | 80,000 |
| 59 ft | 40,000 | 60,000 | 80,000 | 80,000 | 80,000 | 80,000 |
| 60 ft | 40,000 | 60,000 | 80,000 | 80,000 | 80,000 | 80,000 |
Source: FHWA, Bridge Formula Weights; 23 U.S.C. 127 and 23 CFR 658.17. States set their own limits on roads off the Interstate and grandfather some higher figures, and permits override all of these. Check the rules of every state on your route.
Questions
What is the federal bridge formula?
W = 500 [LN/(N − 1) + 12N + 36], where W is the most weight in pounds on any group of two or more consecutive axles, L is the distance in feet between the outer axles of the group and N is the number of axles. W is rounded to the nearest 500 lb. It applies to every group of axles on the vehicle, alongside the 20,000 lb single, 34,000 lb tandem and 80,000 lb gross limits.
How far apart do axles need to be for 80,000 lb?
On a 5-axle truck, 51 ft from the first to the last axle. At 51 ft the formula gives 80,000 lb; at 50 ft only 79,000. The two tandems also need their own spacing: 36 ft or more between the first drive axle and the last trailer axle lets them carry 34,000 lb each.
How many axle groups does the bridge formula check?
Every run of two or more consecutive axles. A 5-axle tractor-trailer has ten: four pairs, three groups of three, two groups of four and the whole vehicle. Each must be at or under its own limit.
What is the weight limit for a tandem axle?
34,000 lb federally, for two axles more than 40 inches and no more than 96 inches apart. Two axles 40 inches apart or less count as a single axle, limited to 20,000 lb.
What is the 36 foot exception?
Two consecutive tandems may carry 34,000 lb each, 68,000 lb in all, if the first and last axles of the two tandems are at least 36 ft apart. The formula alone would only allow 66,000 lb on four axles at 36 ft.
Does the bridge formula apply in every state?
It is the federal standard on the Interstate system. Most states apply it, or something close, on other roads too, but some keep grandfathered limits, different rules for certain trucks such as dump trucks, or permits for heavier loads. Check each state on your route.